python_embed/Lib/site-packages/mne/dipole.py

"""Single-dipole functions and classes."""

# Authors: The MNE-Python contributors.
# License: BSD-3-Clause
# Copyright the MNE-Python contributors.

import functools
import re
from copy import deepcopy
from functools import partial

import numpy as np
from scipy.linalg import eigh
from scipy.optimize import fmin_cobyla

from ._fiff.constants import FIFF
from ._fiff.pick import pick_types
from ._fiff.proj import _needs_eeg_average_ref_proj, make_projector
from ._freesurfer import _get_aseg, head_to_mni, head_to_mri, read_freesurfer_lut
from .bem import ConductorModel, _bem_find_surface, _bem_surf_name, _fit_sphere
from .cov import _ensure_cov, compute_whitener
from .evoked import _aspect_rev, _read_evoked, _write_evokeds
from .fixes import _safe_svd
from .forward._compute_forward import _compute_forwards_meeg, _prep_field_computation
from .forward._make_forward import (
    _get_trans,
    _prep_eeg_channels,
    _prep_meg_channels,
    _setup_bem,
)
from .parallel import parallel_func
from .source_space._source_space import SourceSpaces, _make_volume_source_space
from .surface import _compute_nearest, _points_outside_surface, transform_surface_to
from .transforms import _coord_frame_name, _print_coord_trans, apply_trans
from .utils import (
    ExtendedTimeMixin,
    TimeMixin,
    _check_fname,
    _check_option,
    _get_blas_funcs,
    _pl,
    _repeated_svd,
    _svd_lwork,
    _time_mask,
    _validate_type,
    _verbose_safe_false,
    check_fname,
    copy_function_doc_to_method_doc,
    fill_doc,
    logger,
    pinvh,
    verbose,
    warn,
)
from .viz import plot_dipole_amplitudes, plot_dipole_locations
from .viz.evoked import _plot_evoked


@fill_doc
class Dipole(TimeMixin):
    """Dipole class for sequential dipole fits.

    .. note::
        This class should usually not be instantiated directly via
        ``mne.Dipole(...)``. Instead, use one of the functions
        listed in the See Also section below.

    Used to store positions, orientations, amplitudes, times, goodness of fit
    of dipoles, typically obtained with Neuromag/xfit, mne_dipole_fit
    or certain inverse solvers. Note that dipole position vectors are given in
    the head coordinate frame.

    Parameters
    ----------
    times : array, shape (n_dipoles,)
        The time instants at which each dipole was fitted (s).
    pos : array, shape (n_dipoles, 3)
        The dipoles positions (m) in head coordinates.
    amplitude : array, shape (n_dipoles,)
        The amplitude of the dipoles (Am).
    ori : array, shape (n_dipoles, 3)
        The dipole orientations (normalized to unit length).
    gof : array, shape (n_dipoles,)
        The goodness of fit.
    name : str | None
        Name of the dipole.
    conf : dict
        Confidence limits in dipole orientation for "vol" in m^3 (volume),
        "depth" in m (along the depth axis), "long" in m (longitudinal axis),
        "trans" in m (transverse axis), "qlong" in Am, and "qtrans" in Am
        (currents). The current confidence limit in the depth direction is
        assumed to be zero (although it can be non-zero when a BEM is used).

        .. versionadded:: 0.15
    khi2 : array, shape (n_dipoles,)
        The χ^2 values for the fits.

        .. versionadded:: 0.15
    nfree : array, shape (n_dipoles,)
        The number of free parameters for each fit.

        .. versionadded:: 0.15
    %(verbose)s

    See Also
    --------
    fit_dipole
    DipoleFixed
    read_dipole

    Notes
    -----
    This class is for sequential dipole fits, where the position
    changes as a function of time. For fixed dipole fits, where the
    position is fixed as a function of time, use :class:`mne.DipoleFixed`.
    """

    @verbose
    def __init__(
        self,
        times,
        pos,
        amplitude,
        ori,
        gof,
        name=None,
        conf=None,
        khi2=None,
        nfree=None,
        *,
        verbose=None,
    ):
        self._set_times(np.array(times))
        self._pos = np.array(pos)
        self._amplitude = np.array(amplitude)
        self._ori = np.array(ori)
        self._gof = np.array(gof)
        self._name = name
        self._conf = dict()
        if conf is not None:
            for key, value in conf.items():
                self._conf[key] = np.array(value)
        self._khi2 = np.array(khi2) if khi2 is not None else None
        self._nfree = np.array(nfree) if nfree is not None else None

    def __repr__(self):  # noqa: D105
        s = f"n_times : {len(self.times)}"
        s += f", tmin : {np.min(self.times):0.3f}"
        s += f", tmax : {np.max(self.times):0.3f}"
        return f"<Dipole | {s}>"

    @property
    def pos(self):
        """The dipoles positions (m) in head coordinates."""
        return self._pos

    @property
    def amplitude(self):
        """The amplitude of the dipoles (Am)."""
        return self._amplitude

    @property
    def ori(self):
        """The dipole orientations (normalized to unit length)."""
        return self._ori

    @property
    def gof(self):
        """The goodness of fit."""
        return self._gof

    @property
    def name(self):
        """Name of the dipole."""
        return self._name

    @name.setter
    def name(self, name):
        _validate_type(name, str, "name")
        self._name = name

    @property
    def conf(self):
        """Confidence limits in dipole orientation."""
        return self._conf

    @property
    def khi2(self):
        """The χ^2 values for the fits."""
        return self._khi2

    @property
    def nfree(self):
        """The number of free parameters for each fit."""
        return self._nfree

    @verbose
    def save(self, fname, overwrite=False, *, verbose=None):
        """Save dipole in a ``.dip`` or ``.bdip`` file.

        The ``.[b]dip`` format is for :class:`mne.Dipole` objects, that is,
        fixed-position dipole fits. For these fits, the amplitude, orientation,
        and position vary as a function of time.

        Parameters
        ----------
        fname : path-like
            The name of the ``.dip`` or ``.bdip`` file.
        %(overwrite)s

            .. versionadded:: 0.20
        %(verbose)s

        See Also
        --------
        read_dipole

        Notes
        -----
        .. versionchanged:: 0.20
           Support for writing bdip (Xfit binary) files.
        """
        # obligatory fields
        fname = _check_fname(fname, overwrite=overwrite)
        if fname.suffix == ".bdip":
            _write_dipole_bdip(fname, self)
        else:
            _write_dipole_text(fname, self)

    @verbose
    def crop(self, tmin=None, tmax=None, include_tmax=True, verbose=None):
        """Crop data to a given time interval.

        Parameters
        ----------
        tmin : float | None
            Start time of selection in seconds.
        tmax : float | None
            End time of selection in seconds.
        %(include_tmax)s
        %(verbose)s

        Returns
        -------
        self : instance of Dipole
            The cropped instance.
        """
        sfreq = None
        if len(self.times) > 1:
            sfreq = 1.0 / np.median(np.diff(self.times))
        mask = _time_mask(
            self.times, tmin, tmax, sfreq=sfreq, include_tmax=include_tmax
        )
        self._set_times(self.times[mask])
        for attr in ("_pos", "_gof", "_amplitude", "_ori", "_khi2", "_nfree"):
            if getattr(self, attr) is not None:
                setattr(self, attr, getattr(self, attr)[mask])
        for key in self.conf.keys():
            self.conf[key] = self.conf[key][mask]
        return self

    def copy(self):
        """Copy the Dipoles object.

        Returns
        -------
        dip : instance of Dipole
            The copied dipole instance.
        """
        return deepcopy(self)

    @verbose
    @copy_function_doc_to_method_doc(plot_dipole_locations)
    def plot_locations(
        self,
        trans,
        subject,
        subjects_dir=None,
        mode="orthoview",
        coord_frame="mri",
        idx="gof",
        show_all=True,
        ax=None,
        block=False,
        show=True,
        scale=None,
        color=None,
        *,
        highlight_color="r",
        fig=None,
        title=None,
        head_source="seghead",
        surf="pial",
        width=None,
        verbose=None,
    ):
        return plot_dipole_locations(
            self,
            trans,
            subject,
            subjects_dir,
            mode,
            coord_frame,
            idx,
            show_all,
            ax,
            block,
            show,
            scale=scale,
            color=color,
            highlight_color=highlight_color,
            fig=fig,
            title=title,
            head_source=head_source,
            surf=surf,
            width=width,
        )

    @verbose
    def to_mni(self, subject, trans, subjects_dir=None, verbose=None):
        """Convert dipole location from head to MNI coordinates.

        Parameters
        ----------
        %(subject)s
        %(trans_not_none)s
        %(subjects_dir)s
        %(verbose)s

        Returns
        -------
        pos_mni : array, shape (n_pos, 3)
            The MNI coordinates (in mm) of pos.
        """
        mri_head_t, trans = _get_trans(trans)
        return head_to_mni(
            self.pos, subject, mri_head_t, subjects_dir=subjects_dir, verbose=verbose
        )

    @verbose
    def to_mri(self, subject, trans, subjects_dir=None, verbose=None):
        """Convert dipole location from head to MRI surface RAS coordinates.

        Parameters
        ----------
        %(subject)s
        %(trans_not_none)s
        %(subjects_dir)s
        %(verbose)s

        Returns
        -------
        pos_mri : array, shape (n_pos, 3)
            The Freesurfer surface RAS coordinates (in mm) of pos.
        """
        mri_head_t, trans = _get_trans(trans)
        return head_to_mri(
            self.pos,
            subject,
            mri_head_t,
            subjects_dir=subjects_dir,
            verbose=verbose,
            kind="mri",
        )

    @verbose
    def to_volume_labels(
        self,
        trans,
        subject="fsaverage",
        aseg="aparc+aseg",
        subjects_dir=None,
        verbose=None,
    ):
        """Find an ROI in atlas for the dipole positions.

        Parameters
        ----------
        %(trans)s

            .. versionchanged:: 0.19
                Support for 'fsaverage' argument.
        %(subject)s
        %(aseg)s
        %(subjects_dir)s
        %(verbose)s

        Returns
        -------
        labels : list
            List of anatomical region names from anatomical segmentation atlas.

        Notes
        -----
        .. versionadded:: 0.24
        """
        aseg_img, aseg_data = _get_aseg(aseg, subject, subjects_dir)
        mri_vox_t = np.linalg.inv(aseg_img.header.get_vox2ras_tkr())

        # Load freesurface atlas LUT
        lut_inv = read_freesurfer_lut()[0]
        lut = {v: k for k, v in lut_inv.items()}

        # transform to voxel space from head space
        pos = self.to_mri(subject, trans, subjects_dir=subjects_dir, verbose=verbose)
        pos = apply_trans(mri_vox_t, pos)
        pos = np.rint(pos).astype(int)

        # Get voxel value and label from LUT
        labels = [lut.get(aseg_data[tuple(coord)], "Unknown") for coord in pos]
        return labels

    def plot_amplitudes(self, color="k", show=True):
        """Plot the dipole amplitudes as a function of time.

        Parameters
        ----------
        color : matplotlib color
            Color to use for the trace.
        show : bool
            Show figure if True.

        Returns
        -------
        fig : matplotlib.figure.Figure
            The figure object containing the plot.
        """
        return plot_dipole_amplitudes([self], [color], show)

    def __getitem__(self, item):
        """Get a time slice.

        Parameters
        ----------
        item : array-like or slice
            The slice of time points to use.

        Returns
        -------
        dip : instance of Dipole
            The sliced dipole.
        """
        if isinstance(item, int):  # make sure attributes stay 2d
            item = [item]

        selected_times = self.times[item].copy()
        selected_pos = self.pos[item, :].copy()
        selected_amplitude = self.amplitude[item].copy()
        selected_ori = self.ori[item, :].copy()
        selected_gof = self.gof[item].copy()
        selected_name = self.name
        selected_conf = dict()
        for key in self.conf.keys():
            selected_conf[key] = self.conf[key][item]
        selected_khi2 = self.khi2[item] if self.khi2 is not None else None
        selected_nfree = self.nfree[item] if self.nfree is not None else None
        return Dipole(
            selected_times,
            selected_pos,
            selected_amplitude,
            selected_ori,
            selected_gof,
            selected_name,
            selected_conf,
            selected_khi2,
            selected_nfree,
        )

    def __len__(self):
        """Return the number of dipoles.

        Returns
        -------
        len : int
            The number of dipoles.

        Examples
        --------
        This can be used as::

            >>> len(dipoles)  # doctest: +SKIP
            10
        """
        return self.pos.shape[0]


def _read_dipole_fixed(fname):
    """Read a fixed dipole FIF file."""
    logger.info(f"Reading {fname} ...")
    info, nave, aspect_kind, comment, times, data, _ = _read_evoked(fname)
    return DipoleFixed(info, data, times, nave, aspect_kind, comment=comment)


@fill_doc
class DipoleFixed(ExtendedTimeMixin):
    """Dipole class for fixed-position dipole fits.

    .. note::
        This class should usually not be instantiated directly
        via ``mne.DipoleFixed(...)``. Instead, use one of the functions
        listed in the See Also section below.

    Parameters
    ----------
    %(info_not_none)s
    data : array, shape (n_channels, n_times)
        The dipole data.
    times : array, shape (n_times,)
        The time points.
    nave : int
        Number of averages.
    aspect_kind : int
        The kind of data.
    comment : str
        The dipole comment.
    %(verbose)s

    See Also
    --------
    read_dipole
    Dipole
    fit_dipole

    Notes
    -----
    This class is for fixed-position dipole fits, where the position
    (and maybe orientation) is static over time. For sequential dipole fits,
    where the position can change a function of time, use :class:`mne.Dipole`.

    .. versionadded:: 0.12
    """

    @verbose
    def __init__(
        self, info, data, times, nave, aspect_kind, comment="", *, verbose=None
    ):
        self.info = info
        self.nave = nave
        self._aspect_kind = aspect_kind
        self.kind = _aspect_rev.get(aspect_kind, "unknown")
        self.comment = comment
        self._set_times(np.array(times))
        self.data = data
        self.preload = True
        self._update_first_last()

    def __repr__(self):  # noqa: D105
        s = f"n_times : {len(self.times)}"
        s += f", tmin : {np.min(self.times)}"
        s += f", tmax : {np.max(self.times)}"
        return f"<DipoleFixed | {s}>"

    def copy(self):
        """Copy the DipoleFixed object.

        Returns
        -------
        inst : instance of DipoleFixed
            The copy.

        Notes
        -----
        .. versionadded:: 0.16
        """
        return deepcopy(self)

    @property
    def ch_names(self):
        """Channel names."""
        return self.info["ch_names"]

    @verbose
    def save(self, fname, *, overwrite=False, verbose=None):
        """Save fixed dipole in FIF format.

        The ``.fif[.gz]`` format is for :class:`mne.DipoleFixed` objects, that is,
        fixed-position and optionally fixed-orientation dipole fits. For these fits,
        the amplitude (and optionally orientation) vary as a function of time,
        but not the position.

        Parameters
        ----------
        fname : path-like
            The name of the FIF file. Must end with ``'-dip.fif'`` or
            ``'-dip.fif.gz'`` to make it explicit that the file contains
            dipole information in FIF format.
        %(overwrite)s

            .. versionadded:: 1.10.0
        %(verbose)s

        See Also
        --------
        read_dipole
        """
        check_fname(
            fname,
            "DipoleFixed",
            (
                "-dip.fif",
                "-dip.fif.gz",
                "_dip.fif",
                "_dip.fif.gz",
            ),
            (".fif", ".fif.gz"),
        )
        _write_evokeds(fname, self, check=False, overwrite=overwrite)

    def plot(self, show=True, time_unit="s"):
        """Plot dipole data.

        Parameters
        ----------
        show : bool
            Call pyplot.show() at the end or not.
        time_unit : str
            The units for the time axis, can be "ms" or "s" (default).

            .. versionadded:: 0.16

        Returns
        -------
        fig : instance of matplotlib.figure.Figure
            The figure containing the time courses.
        """
        return _plot_evoked(
            self,
            picks=None,
            exclude=(),
            unit=True,
            show=show,
            ylim=None,
            xlim="tight",
            proj=False,
            hline=None,
            units=None,
            scalings=None,
            titles=None,
            axes=None,
            gfp=False,
            window_title=None,
            spatial_colors=False,
            plot_type="butterfly",
            selectable=False,
            time_unit=time_unit,
        )


# #############################################################################
# IO
@verbose
def read_dipole(fname, verbose=None):
    """Read a dipole object from a file.

    Non-fixed-position :class:`mne.Dipole` objects are usually saved in ``.[b]dip``
    format. Fixed-position :class:`mne.DipoleFixed` objects are usually saved in
    FIF format.

    Parameters
    ----------
    fname : path-like
        The name of the ``.[b]dip`` or ``.fif[.gz]`` file.
    %(verbose)s

    Returns
    -------
    %(dipole)s

    See Also
    --------
    Dipole
    DipoleFixed
    fit_dipole

    Notes
    -----
    .. versionchanged:: 0.20
       Support for reading bdip (Xfit binary) format.
    """
    fname = _check_fname(fname, overwrite="read", must_exist=True)
    if fname.suffix == ".fif" or fname.name.endswith(".fif.gz"):
        return _read_dipole_fixed(fname)
    elif fname.suffix == ".bdip":
        return _read_dipole_bdip(fname)
    else:
        return _read_dipole_text(fname)


def _read_dipole_text(fname):
    """Read a dipole text file."""
    # Figure out the special fields
    need_header = True
    def_line = name = None
    # There is a bug in older np.loadtxt regarding skipping fields,
    # so just read the data ourselves (need to get name and header anyway)
    data = list()
    with open(fname) as fid:
        for line in fid:
            if not (line.startswith("%") or line.startswith("#")):
                need_header = False
                data.append(line.strip().split())
            else:
                if need_header:
                    def_line = line
                if line.startswith("##") or line.startswith("%%"):
                    m = re.search('Name "(.*) dipoles"', line)
                    if m:
                        name = m.group(1)
        del line
    data = np.atleast_2d(np.array(data, float))
    if def_line is None:
        raise OSError(
            "Dipole text file is missing field definition comment, cannot parse "
            f"{fname}"
        )
    # actually parse the fields
    def_line = def_line.lstrip("%").lstrip("#").strip()
    # MNE writes it out differently than Elekta, let's standardize them...
    fields = re.sub(
        r"([X|Y|Z] )\(mm\)",  # "X (mm)", etc.
        lambda match: match.group(1).strip() + "/mm",
        def_line,
    )
    fields = re.sub(
        r"\((.*?)\)",
        lambda match: "/" + match.group(1),
        fields,  # "Q(nAm)", etc.
    )
    fields = re.sub(
        "(begin|end) ",  # "begin" and "end" with no units
        lambda match: match.group(1) + "/ms",
        fields,
    )
    fields = fields.lower().split()
    required_fields = (
        "begin/ms",
        "x/mm",
        "y/mm",
        "z/mm",
        "q/nam",
        "qx/nam",
        "qy/nam",
        "qz/nam",
        "g/%",
    )
    optional_fields = (
        "khi^2",
        "free",  # standard ones
        # now the confidence fields (up to 5!)
        "vol/mm^3",
        "depth/mm",
        "long/mm",
        "trans/mm",
        "qlong/nam",
        "qtrans/nam",
    )
    conf_scales = [1e-9, 1e-3, 1e-3, 1e-3, 1e-9, 1e-9]
    missing_fields = sorted(set(required_fields) - set(fields))
    if len(missing_fields) > 0:
        raise RuntimeError(
            f"Could not find necessary fields in header: {missing_fields}"
        )
    handled_fields = set(required_fields) | set(optional_fields)
    assert len(handled_fields) == len(required_fields) + len(optional_fields)
    ignored_fields = sorted(set(fields) - set(handled_fields) - {"end/ms"})
    if len(ignored_fields) > 0:
        warn(f"Ignoring extra fields in dipole file: {ignored_fields}")
    if len(fields) != data.shape[1]:
        raise OSError(
            f"More data fields ({len(fields)}) found than data columns ({data.shape[1]}"
            f"): {fields}"
        )

    logger.info(f"{len(data)} dipole(s) found")

    if "end/ms" in fields:
        if np.diff(
            data[:, [fields.index("begin/ms"), fields.index("end/ms")]], 1, -1
        ).any():
            warn(
                "begin and end fields differed, but only begin will be used "
                "to store time values"
            )

    # Find the correct column in our data array, then scale to proper units
    idx = [fields.index(field) for field in required_fields]
    assert len(idx) >= 9
    times = data[:, idx[0]] / 1000.0
    pos = 1e-3 * data[:, idx[1:4]]  # put data in meters
    amplitude = data[:, idx[4]]
    norm = amplitude.copy()
    amplitude /= 1e9
    norm[norm == 0] = 1
    ori = data[:, idx[5:8]] / norm[:, np.newaxis]
    gof = data[:, idx[8]]
    # Deal with optional fields
    optional = [None] * 2
    for fi, field in enumerate(optional_fields[:2]):
        if field in fields:
            optional[fi] = data[:, fields.index(field)]
    khi2, nfree = optional
    conf = dict()
    for field, scale in zip(optional_fields[2:], conf_scales):  # confidence
        if field in fields:
            conf[field.split("/")[0]] = scale * data[:, fields.index(field)]
    return Dipole(times, pos, amplitude, ori, gof, name, conf, khi2, nfree)


def _write_dipole_text(fname, dip):
    fmt = "  %7.1f %7.1f %8.2f %8.2f %8.2f %8.3f %8.3f %8.3f %8.3f %6.2f"
    header = (
        "#   begin     end   X (mm)   Y (mm)   Z (mm)"
        "   Q(nAm)  Qx(nAm)  Qy(nAm)  Qz(nAm)    g/%"
    )
    t = dip.times[:, np.newaxis] * 1000.0
    gof = dip.gof[:, np.newaxis]
    amp = 1e9 * dip.amplitude[:, np.newaxis]
    out = (t, t, dip.pos / 1e-3, amp, dip.ori * amp, gof)

    # optional fields
    fmts = dict(
        khi2=("    khi^2", " %8.1f", 1.0),
        nfree=("  free", " %5d", 1),
        vol=("  vol/mm^3", " %9.3f", 1e9),
        depth=("  depth/mm", " %9.3f", 1e3),
        long=("  long/mm", " %8.3f", 1e3),
        trans=("  trans/mm", " %9.3f", 1e3),
        qlong=("  Qlong/nAm", " %10.3f", 1e9),
        qtrans=("  Qtrans/nAm", " %11.3f", 1e9),
    )
    for key in ("khi2", "nfree"):
        data = getattr(dip, key)
        if data is not None:
            header += fmts[key][0]
            fmt += fmts[key][1]
            out += (data[:, np.newaxis] * fmts[key][2],)
    for key in ("vol", "depth", "long", "trans", "qlong", "qtrans"):
        data = dip.conf.get(key)
        if data is not None:
            header += fmts[key][0]
            fmt += fmts[key][1]
            out += (data[:, np.newaxis] * fmts[key][2],)
    out = np.concatenate(out, axis=-1)

    # NB CoordinateSystem is hard-coded as Head here
    with open(fname, "wb") as fid:
        fid.write(b'# CoordinateSystem "Head"\n')
        fid.write((header + "\n").encode("utf-8"))
        np.savetxt(fid, out, fmt=fmt)
        if dip.name is not None:
            fid.write((f'## Name "{dip.name} dipoles" Style "Dipoles"').encode())


_BDIP_ERROR_KEYS = ("depth", "long", "trans", "qlong", "qtrans")


def _read_dipole_bdip(fname):
    name = None
    nfree = None
    with open(fname, "rb") as fid:
        # Which dipole in a multi-dipole set
        times = list()
        pos = list()
        amplitude = list()
        ori = list()
        gof = list()
        conf = dict(vol=list())
        khi2 = list()
        has_errors = None
        while True:
            num = np.frombuffer(fid.read(4), ">i4")
            if len(num) == 0:
                break
            times.append(np.frombuffer(fid.read(4), ">f4")[0])
            fid.read(4)  # end
            fid.read(12)  # r0
            pos.append(np.frombuffer(fid.read(12), ">f4"))
            Q = np.frombuffer(fid.read(12), ">f4")
            amplitude.append(np.linalg.norm(Q))
            ori.append(Q / amplitude[-1])
            gof.append(100 * np.frombuffer(fid.read(4), ">f4")[0])
            this_has_errors = bool(np.frombuffer(fid.read(4), ">i4")[0])
            if has_errors is None:
                has_errors = this_has_errors
                for key in _BDIP_ERROR_KEYS:
                    conf[key] = list()
            assert has_errors == this_has_errors
            fid.read(4)  # Noise level used for error computations
            limits = np.frombuffer(fid.read(20), ">f4")  # error limits
            for key, lim in zip(_BDIP_ERROR_KEYS, limits):
                conf[key].append(lim)
            fid.read(100)  # (5, 5) fully describes the conf. ellipsoid
            conf["vol"].append(np.frombuffer(fid.read(4), ">f4")[0])
            khi2.append(np.frombuffer(fid.read(4), ">f4")[0])
            fid.read(4)  # prob
            fid.read(4)  # total noise estimate
    return Dipole(times, pos, amplitude, ori, gof, name, conf, khi2, nfree)


def _write_dipole_bdip(fname, dip):
    with open(fname, "wb+") as fid:
        for ti, t in enumerate(dip.times):
            fid.write(np.zeros(1, ">i4").tobytes())  # int dipole
            fid.write(np.array([t, 0]).astype(">f4").tobytes())
            fid.write(np.zeros(3, ">f4").tobytes())  # r0
            fid.write(dip.pos[ti].astype(">f4").tobytes())  # pos
            Q = dip.amplitude[ti] * dip.ori[ti]
            fid.write(Q.astype(">f4").tobytes())
            fid.write(np.array(dip.gof[ti] / 100.0, ">f4").tobytes())
            has_errors = int(bool(len(dip.conf)))
            fid.write(np.array(has_errors, ">i4").tobytes())  # has_errors
            fid.write(np.zeros(1, ">f4").tobytes())  # noise level
            for key in _BDIP_ERROR_KEYS:
                val = dip.conf[key][ti] if key in dip.conf else 0.0
                assert val.shape == ()
                fid.write(np.array(val, ">f4").tobytes())
            fid.write(np.zeros(25, ">f4").tobytes())
            conf = dip.conf["vol"][ti] if "vol" in dip.conf else 0.0
            fid.write(np.array(conf, ">f4").tobytes())
            khi2 = dip.khi2[ti] if dip.khi2 is not None else 0
            fid.write(np.array(khi2, ">f4").tobytes())
            fid.write(np.zeros(1, ">f4").tobytes())  # prob
            fid.write(np.zeros(1, ">f4").tobytes())  # total noise est


# #############################################################################
# Fitting


def _dipole_forwards(*, sensors, fwd_data, whitener, rr, n_jobs=None):
    """Compute the forward solution and do other nice stuff."""
    B = _compute_forwards_meeg(
        rr, sensors=sensors, fwd_data=fwd_data, n_jobs=n_jobs, silent=True
    )
    B = np.concatenate(list(B.values()), axis=1)
    assert np.isfinite(B).all()
    B_orig = B.copy()

    # Apply projection and whiten (cov has projections already)
    _, _, dgemm = _get_ddot_dgemv_dgemm()
    B = dgemm(1.0, B, whitener.T)

    # column normalization doesn't affect our fitting, so skip for now
    # S = np.sum(B * B, axis=1)  # across channels
    # scales = np.repeat(3. / np.sqrt(np.sum(np.reshape(S, (len(rr), 3)),
    #                                        axis=1)), 3)
    # B *= scales[:, np.newaxis]
    scales = np.ones(3)
    return B, B_orig, scales


@verbose
def _make_guesses(surf, grid, exclude, mindist, n_jobs=None, verbose=None):
    """Make a guess space inside a sphere or BEM surface."""
    if "rr" in surf:
        logger.info(
            "Guess surface ({}) is in {} coordinates".format(
                _bem_surf_name[surf["id"]], _coord_frame_name(surf["coord_frame"])
            )
        )
    else:
        logger.info(
            f"Making a spherical guess space with radius {1000 * surf.radius:7.1f} "
            "mm..."
        )
    logger.info("Filtering (grid = %6.f mm)..." % (1000 * grid))
    src = _make_volume_source_space(
        surf, grid, exclude, 1000 * mindist, do_neighbors=False, n_jobs=n_jobs
    )[0]
    assert "vertno" in src
    # simplify the result to make things easier later
    src = dict(
        rr=src["rr"][src["vertno"]],
        nn=src["nn"][src["vertno"]],
        nuse=src["nuse"],
        coord_frame=src["coord_frame"],
        vertno=np.arange(src["nuse"]),
        type="discrete",
    )
    return SourceSpaces([src])


def _fit_eval(rd, B, B2, *, sensors, fwd_data, whitener, lwork, fwd_svd):
    """Calculate the residual sum of squares."""
    if fwd_svd is None:
        assert sensors is not None
        fwd = _dipole_forwards(
            sensors=sensors, fwd_data=fwd_data, whitener=whitener, rr=rd[np.newaxis, :]
        )[0]
        uu, sing, vv = _repeated_svd(fwd, lwork, overwrite_a=True)
    else:
        uu, sing, vv = fwd_svd
    gof = _dipole_gof(uu, sing, vv, B, B2)[0]
    # mne-c uses fitness=B2-Bm2, but ours (1-gof) is just a normalized version
    return 1.0 - gof


@functools.lru_cache(None)
def _get_ddot_dgemv_dgemm():
    return _get_blas_funcs(np.float64, ("dot", "gemv", "gemm"))


def _dipole_gof(uu, sing, vv, B, B2):
    """Calculate the goodness of fit from the forward SVD."""
    ddot, dgemv, _ = _get_ddot_dgemv_dgemm()
    ncomp = 3 if sing[2] / (sing[0] if sing[0] > 0 else 1.0) > 0.2 else 2
    one = dgemv(1.0, vv[:ncomp], B)  # np.dot(vv[:ncomp], B)
    Bm2 = ddot(one, one)  # np.sum(one * one)
    gof = Bm2 / B2
    return gof, one


def _fit_Q(*, sensors, fwd_data, whitener, B, B2, B_orig, rd, ori=None):
    """Fit the dipole moment once the location is known."""
    if "fwd" in fwd_data:
        # should be a single precomputed "guess" (i.e., fixed position)
        assert rd is None
        fwd = fwd_data["fwd"]
        assert fwd.shape[0] == 3
        fwd_orig = fwd_data["fwd_orig"]
        assert fwd_orig.shape[0] == 3
        scales = fwd_data["scales"]
        assert scales.shape == (3,)
        fwd_svd = fwd_data["fwd_svd"][0]
    else:
        fwd, fwd_orig, scales = _dipole_forwards(
            sensors=sensors, fwd_data=fwd_data, whitener=whitener, rr=rd[np.newaxis, :]
        )
        fwd_svd = None
    if ori is None:
        if fwd_svd is None:
            fwd_svd = _safe_svd(fwd, full_matrices=False)
        uu, sing, vv = fwd_svd
        gof, one = _dipole_gof(uu, sing, vv, B, B2)
        ncomp = len(one)
        one /= sing[:ncomp]
        Q = np.dot(one, uu.T[:ncomp])
    else:
        fwd = np.dot(ori[np.newaxis], fwd)
        sing = np.linalg.norm(fwd)
        one = np.dot(fwd / sing, B)
        gof = (one * one)[0] / B2
        Q = ori * np.sum(one / sing)
        ncomp = 3
    # Counteract the effect of column normalization
    Q *= scales[0]
    B_residual_noproj = B_orig - np.dot(fwd_orig.T, Q)
    return Q, gof, B_residual_noproj, ncomp


def _fit_dipoles(
    fun,
    min_dist_to_inner_skull,
    data,
    times,
    guess_rrs,
    guess_data,
    *,
    sensors,
    fwd_data,
    whitener,
    ori,
    n_jobs,
    rank,
    rhoend,
):
    """Fit a single dipole to the given whitened, projected data."""
    parallel, p_fun, n_jobs = parallel_func(fun, n_jobs)
    # parallel over time points
    res = parallel(
        p_fun(
            min_dist_to_inner_skull,
            B,
            t,
            guess_rrs,
            guess_data,
            sensors=sensors,
            fwd_data=fwd_data,
            whitener=whitener,
            fmin_cobyla=fmin_cobyla,
            ori=ori,
            rank=rank,
            rhoend=rhoend,
        )
        for B, t in zip(data.T, times)
    )
    pos = np.array([r[0] for r in res])
    amp = np.array([r[1] for r in res])
    ori = np.array([r[2] for r in res])
    gof = np.array([r[3] for r in res]) * 100  # convert to percentage
    conf = None
    if res[0][4] is not None:
        conf = np.array([r[4] for r in res])
        keys = ["vol", "depth", "long", "trans", "qlong", "qtrans"]
        conf = {key: conf[:, ki] for ki, key in enumerate(keys)}
    khi2 = np.array([r[5] for r in res])
    nfree = np.array([r[6] for r in res])
    residual_noproj = np.array([r[7] for r in res]).T

    return pos, amp, ori, gof, conf, khi2, nfree, residual_noproj


'''Simplex code in case we ever want/need it for testing

def _make_tetra_simplex():
    """Make the initial tetrahedron"""
    #
    # For this definition of a regular tetrahedron, see
    #
    # http://mathworld.wolfram.com/Tetrahedron.html
    #
    x = np.sqrt(3.0) / 3.0
    r = np.sqrt(6.0) / 12.0
    R = 3 * r
    d = x / 2.0
    simplex = 1e-2 * np.array([[x, 0.0, -r],
                               [-d, 0.5, -r],
                               [-d, -0.5, -r],
                               [0., 0., R]])
    return simplex


def try_(p, y, psum, ndim, fun, ihi, neval, fac):
    """Helper to try a value"""
    ptry = np.empty(ndim)
    fac1 = (1.0 - fac) / ndim
    fac2 = fac1 - fac
    ptry = psum * fac1 - p[ihi] * fac2
    ytry = fun(ptry)
    neval += 1
    if ytry < y[ihi]:
        y[ihi] = ytry
        psum[:] += ptry - p[ihi]
        p[ihi] = ptry
    return ytry, neval


def _simplex_minimize(p, ftol, stol, fun, max_eval=1000):
    """Minimization with the simplex algorithm

    Modified from Numerical recipes"""
    y = np.array([fun(s) for s in p])
    ndim = p.shape[1]
    assert p.shape[0] == ndim + 1
    mpts = ndim + 1
    neval = 0
    psum = p.sum(axis=0)

    loop = 1
    while(True):
        ilo = 1
        if y[1] > y[2]:
            ihi = 1
            inhi = 2
        else:
            ihi = 2
            inhi = 1
        for i in range(mpts):
            if y[i] < y[ilo]:
                ilo = i
            if y[i] > y[ihi]:
                inhi = ihi
                ihi = i
            elif y[i] > y[inhi]:
                if i != ihi:
                    inhi = i

        rtol = 2 * np.abs(y[ihi] - y[ilo]) / (np.abs(y[ihi]) + np.abs(y[ilo]))
        if rtol < ftol:
            break
        if neval >= max_eval:
            raise RuntimeError('Maximum number of evaluations exceeded.')
        if stol > 0:  # Has the simplex collapsed?
            dsum = np.sqrt(np.sum((p[ilo] - p[ihi]) ** 2))
            if loop > 5 and dsum < stol:
                break

        ytry, neval = try_(p, y, psum, ndim, fun, ihi, neval, -1.)
        if ytry <= y[ilo]:
            ytry, neval = try_(p, y, psum, ndim, fun, ihi, neval, 2.)
        elif ytry >= y[inhi]:
            ysave = y[ihi]
            ytry, neval = try_(p, y, psum, ndim, fun, ihi, neval, 0.5)
            if ytry >= ysave:
                for i in range(mpts):
                    if i != ilo:
                        psum[:] = 0.5 * (p[i] + p[ilo])
                        p[i] = psum
                        y[i] = fun(psum)
                neval += ndim
                psum = p.sum(axis=0)
        loop += 1
'''


def _fit_confidence(*, rd, Q, ori, whitener, fwd_data, sensors):
    # As describedd in the Xfit manual, confidence intervals can be calculated
    # by examining a linearization of model at the best-fitting location,
    # i.e. taking the Jacobian and using the whitener:
    #
    #     J = [∂b/∂x ∂b/∂y ∂b/∂z ∂b/∂Qx ∂b/∂Qy ∂b/∂Qz]
    #     C = (J.T C^-1 J)^-1
    #
    # And then the confidence interval is the diagonal of C, scaled by 1.96
    # (for 95% confidence).
    direction = np.empty((3, 3))
    # The coordinate system has the x axis aligned with the dipole orientation,
    direction[0] = ori
    # the z axis through the origin of the sphere model
    rvec = rd - fwd_data["inner_skull"]["r0"]
    direction[2] = rvec - ori * np.dot(ori, rvec)  # orthogonalize
    direction[2] /= np.linalg.norm(direction[2])
    # and the y axis perpendical with these forming a right-handed system.
    direction[1] = np.cross(direction[2], direction[0])
    assert np.allclose(np.dot(direction, direction.T), np.eye(3))
    # Get spatial deltas in dipole coordinate directions
    deltas = (-1e-4, 1e-4)
    J = np.empty((whitener.shape[0], 6))
    for ii in range(3):
        fwds = []
        for delta in deltas:
            this_r = rd[np.newaxis] + delta * direction[ii]
            fwds.append(
                np.dot(
                    Q,
                    _dipole_forwards(
                        sensors=sensors, fwd_data=fwd_data, whitener=whitener, rr=this_r
                    )[0],
                )
            )
        J[:, ii] = np.diff(fwds, axis=0)[0] / np.diff(deltas)[0]
    # Get current (Q) deltas in the dipole directions
    deltas = np.array([-0.01, 0.01]) * np.linalg.norm(Q)
    this_fwd = _dipole_forwards(
        sensors=sensors, fwd_data=fwd_data, whitener=whitener, rr=rd[np.newaxis]
    )[0]
    for ii in range(3):
        fwds = []
        for delta in deltas:
            fwds.append(np.dot(Q + delta * direction[ii], this_fwd))
        J[:, ii + 3] = np.diff(fwds, axis=0)[0] / np.diff(deltas)[0]
    # J is already whitened, so we don't need to do np.dot(whitener, J).
    # However, the units in the Jacobian are potentially quite different,
    # so we need to do some normalization during inversion, then revert.
    direction_norm = np.linalg.norm(J[:, :3])
    Q_norm = np.linalg.norm(J[:, 3:5])  # omit possible zero Z
    norm = np.array([direction_norm] * 3 + [Q_norm] * 3)
    J /= norm
    J = np.dot(J.T, J)
    C = pinvh(J, rtol=1e-14)
    C /= norm
    C /= norm[:, np.newaxis]
    conf = 1.96 * np.sqrt(np.diag(C))
    # The confidence volume of the dipole location is obtained from by
    # taking the eigenvalues of the upper left submatrix and computing
    # v = 4π/3 √(c^3 λ1 λ2 λ3) with c = 7.81, or:
    vol_conf = (
        4
        * np.pi
        / 3.0
        * np.sqrt(476.379541 * np.prod(eigh(C[:3, :3], eigvals_only=True)))
    )
    conf = np.concatenate([conf, [vol_conf]])
    # Now we reorder and subselect the proper columns:
    # vol, depth, long, trans, Qlong, Qtrans (discard Qdepth, assumed zero)
    conf = conf[[6, 2, 0, 1, 3, 4]]
    return conf


def _surface_constraint(rd, surf, min_dist_to_inner_skull):
    """Surface fitting constraint."""
    dist = _compute_nearest(surf["rr"], rd[np.newaxis, :], return_dists=True)[1][0]
    if _points_outside_surface(rd[np.newaxis, :], surf, 1)[0]:
        dist *= -1.0
    # Once we know the dipole is below the inner skull,
    # let's check if its distance to the inner skull is at least
    # min_dist_to_inner_skull. This can be enforced by adding a
    # constrain proportional to its distance.
    dist -= min_dist_to_inner_skull
    return dist


def _sphere_constraint(rd, r0, R_adj):
    """Sphere fitting constraint."""
    return R_adj - np.sqrt(np.sum((rd - r0) ** 2))


def _fit_dipole(
    min_dist_to_inner_skull,
    B_orig,
    t,
    guess_rrs,
    guess_data,
    *,
    sensors,
    fwd_data,
    whitener,
    fmin_cobyla,
    ori,
    rank,
    rhoend,
):
    """Fit a single bit of data."""
    B = np.dot(whitener, B_orig)

    # make constraint function to keep the solver within the inner skull
    if "rr" in fwd_data["inner_skull"]:  # bem
        surf = fwd_data["inner_skull"]
        constraint = partial(
            _surface_constraint,
            surf=surf,
            min_dist_to_inner_skull=min_dist_to_inner_skull,
        )
    else:  # sphere
        surf = None
        constraint = partial(
            _sphere_constraint,
            r0=fwd_data["inner_skull"]["r0"],
            R_adj=fwd_data["inner_skull"].radius - min_dist_to_inner_skull,
        )

    # Find a good starting point (find_best_guess in C)
    B2 = np.dot(B, B)
    if B2 == 0:
        warn(f"Zero field found for time {t}")
        return np.zeros(3), 0, np.zeros(3), 0, B

    idx = np.argmin(
        [
            _fit_eval(
                guess_rrs[[fi], :],
                B,
                B2,
                fwd_svd=fwd_svd,
                fwd_data=None,
                sensors=None,
                whitener=None,
                lwork=None,
            )
            for fi, fwd_svd in enumerate(guess_data["fwd_svd"])
        ]
    )
    x0 = guess_rrs[idx]
    lwork = _svd_lwork((3, B.shape[0]))
    fun = partial(
        _fit_eval,
        B=B,
        B2=B2,
        fwd_data=fwd_data,
        whitener=whitener,
        lwork=lwork,
        sensors=sensors,
        fwd_svd=None,
    )

    # Tested minimizers:
    #    Simplex, BFGS, CG, COBYLA, L-BFGS-B, Powell, SLSQP, TNC
    # Several were similar, but COBYLA won for having a handy constraint
    # function we can use to ensure we stay inside the inner skull /
    # smallest sphere
    rd_final = fmin_cobyla(
        fun, x0, (constraint,), consargs=(), rhobeg=5e-2, rhoend=rhoend, disp=False
    )

    # simplex = _make_tetra_simplex() + x0
    # _simplex_minimize(simplex, 1e-4, 2e-4, fun)
    # rd_final = simplex[0]

    # Compute the dipole moment at the final point
    Q, gof, residual_noproj, n_comp = _fit_Q(
        sensors=sensors,
        fwd_data=fwd_data,
        whitener=whitener,
        B=B,
        B2=B2,
        B_orig=B_orig,
        rd=rd_final,
        ori=ori,
    )
    khi2 = (1 - gof) * B2
    nfree = rank - n_comp
    amp = np.sqrt(np.dot(Q, Q))
    norm = 1.0 if amp == 0.0 else amp
    ori = Q / norm

    conf = _fit_confidence(
        sensors=sensors, rd=rd_final, Q=Q, ori=ori, whitener=whitener, fwd_data=fwd_data
    )

    msg = "---- Fitted : %7.1f ms" % (1000.0 * t)
    if surf is not None:
        dist_to_inner_skull = _compute_nearest(
            surf["rr"], rd_final[np.newaxis, :], return_dists=True
        )[1][0]
        msg += ", distance to inner skull : %2.4f mm" % (dist_to_inner_skull * 1000.0)

    logger.info(msg)
    return rd_final, amp, ori, gof, conf, khi2, nfree, residual_noproj


def _fit_dipole_fixed(
    min_dist_to_inner_skull,
    B_orig,
    t,
    guess_rrs,
    guess_data,
    *,
    sensors,
    fwd_data,
    whitener,
    fmin_cobyla,
    ori,
    rank,
    rhoend,
):
    """Fit a data using a fixed position."""
    B = np.dot(whitener, B_orig)
    B2 = np.dot(B, B)
    if B2 == 0:
        warn(f"Zero field found for time {t}")
        return np.zeros(3), 0, np.zeros(3), 0, np.zeros(6)
    # Compute the dipole moment
    Q, gof, residual_noproj = _fit_Q(
        fwd_data=guess_data,
        whitener=whitener,
        B=B,
        B2=B2,
        B_orig=B_orig,
        sensors=sensors,
        rd=None,
        ori=ori,
    )[:3]
    if ori is None:
        amp = np.sqrt(np.dot(Q, Q))
        norm = 1.0 if amp == 0.0 else amp
        ori = Q / norm
    else:
        amp = np.dot(Q, ori)
    rd_final = guess_rrs[0]
    # This will be slow, and we don't use it anyway, so omit it for now:
    # conf = _fit_confidence(rd_final, Q, ori, whitener, fwd_data)
    conf = khi2 = nfree = None
    # No corresponding 'logger' message here because it should go *very* fast
    return rd_final, amp, ori, gof, conf, khi2, nfree, residual_noproj


@verbose
def fit_dipole(
    evoked,
    cov,
    bem,
    trans=None,
    min_dist=5.0,
    n_jobs=None,
    pos=None,
    ori=None,
    rank=None,
    accuracy="normal",
    tol=5e-5,
    verbose=None,
):
    """Fit a dipole.

    Parameters
    ----------
    evoked : instance of Evoked
        The dataset to fit.
    cov : str | instance of Covariance
        The noise covariance.
    bem : path-like | instance of ConductorModel
        The BEM filename (str) or conductor model.
    trans : path-like | None
        The head<->MRI transform filename. Must be provided unless BEM
        is a sphere model.
    min_dist : float
        Minimum distance (in millimeters) from the dipole to the inner skull.
        Must be positive. Note that because this is a constraint passed to
        a solver it is not strict but close, i.e. for a ``min_dist=5.`` the
        fits could be 4.9 mm from the inner skull.
    %(n_jobs)s
        It is used in field computation and fitting.
    pos : ndarray, shape (3,) | None
        Position of the dipole to use. If None (default), sequential
        fitting (different position and orientation for each time instance)
        is performed. If a position (in head coords) is given as an array,
        the position is fixed during fitting.

        .. versionadded:: 0.12
    ori : ndarray, shape (3,) | None
        Orientation of the dipole to use. If None (default), the
        orientation is free to change as a function of time. If an
        orientation (in head coordinates) is given as an array, ``pos``
        must also be provided, and the routine computes the amplitude and
        goodness of fit of the dipole at the given position and orientation
        for each time instant.

        .. versionadded:: 0.12
    %(rank_none)s

        .. versionadded:: 0.20
    accuracy : str
        Can be ``"normal"`` (default) or ``"accurate"``, which gives the most
        accurate coil definition but is typically not necessary for real-world
        data.

        .. versionadded:: 0.24
    tol : float
        Final accuracy of the optimization (see ``rhoend`` argument of
        :func:`scipy.optimize.fmin_cobyla`).

        .. versionadded:: 0.24
    %(verbose)s

    Returns
    -------
    dip : instance of Dipole or DipoleFixed
        The dipole fits. A :class:`mne.DipoleFixed` is returned if
        ``pos`` and ``ori`` are both not None, otherwise a
        :class:`mne.Dipole` is returned.
    residual : instance of Evoked
        The M-EEG data channels with the fitted dipolar activity removed.

    See Also
    --------
    mne.beamformer.rap_music
    Dipole
    DipoleFixed
    read_dipole

    Notes
    -----
    .. versionadded:: 0.9.0
    """
    # This could eventually be adapted to work with other inputs, these
    # are what is needed:

    evoked = evoked.copy()
    _validate_type(accuracy, str, "accuracy")
    _check_option("accuracy", accuracy, ("accurate", "normal"))

    # Determine if a list of projectors has an average EEG ref
    if _needs_eeg_average_ref_proj(evoked.info):
        raise ValueError("EEG average reference is mandatory for dipole fitting.")
    if min_dist < 0:
        raise ValueError(f"min_dist should be positive. Got {min_dist}")
    if ori is not None and pos is None:
        raise ValueError("pos must be provided if ori is not None")

    data = evoked.data
    if not np.isfinite(data).all():
        raise ValueError("Evoked data must be finite")
    info = evoked.info
    times = evoked.times.copy()
    comment = evoked.comment

    # Convert the min_dist to meters
    min_dist_to_inner_skull = min_dist / 1000.0
    del min_dist

    # Figure out our inputs
    neeg = len(pick_types(info, meg=False, eeg=True, ref_meg=False, exclude=[]))
    if isinstance(bem, str):
        bem_extra = bem
    else:
        bem_extra = repr(bem)
        logger.info(f"BEM               : {bem_extra}")
    mri_head_t, trans = _get_trans(trans)
    logger.info(f"MRI transform     : {trans}")
    safe_false = _verbose_safe_false()
    bem = _setup_bem(bem, bem_extra, neeg, mri_head_t, verbose=safe_false)
    if not bem["is_sphere"]:
        # Find the best-fitting sphere
        inner_skull = _bem_find_surface(bem, "inner_skull")
        inner_skull = inner_skull.copy()
        R, r0 = _fit_sphere(inner_skull["rr"])
        # r0 back to head frame for logging
        r0 = apply_trans(mri_head_t["trans"], r0[np.newaxis, :])[0]
        inner_skull["r0"] = r0
        logger.info(
            f"Head origin       : {1000 * r0[0]:6.1f} {1000 * r0[1]:6.1f} "
            f"{1000 * r0[2]:6.1f} mm rad = {1000 * R:6.1f} mm."
        )
        del R, r0
    else:
        r0 = bem["r0"]
        if len(bem.get("layers", [])) > 0:
            R = bem["layers"][0]["rad"]
            kind = "rad"
        else:  # MEG-only
            # Use the minimum distance to the MEG sensors as the radius then
            R = np.dot(
                np.linalg.inv(info["dev_head_t"]["trans"]), np.hstack([r0, [1.0]])
            )[:3]  # r0 -> device
            R = R - [
                info["chs"][pick]["loc"][:3]
                for pick in pick_types(info, meg=True, exclude=[])
            ]
            if len(R) == 0:
                raise RuntimeError(
                    "No MEG channels found, but MEG-only sphere model used"
                )
            R = np.min(np.linalg.norm(R, axis=1))
            kind = "min_rad"
        logger.info(
            f"Sphere model      : origin at ({1000 * r0[0]: 7.2f} {1000 * r0[1]: 7.2f} "
            f"{1000 * r0[2]: 7.2f}) mm, {kind} = {R:6.1f} mm"
        )
        # NB sphere model defined in head frame
        inner_skull = ConductorModel(layers=[dict(rad=R)], r0=r0, is_sphere=True)
        del R, r0

    # Deal with DipoleFixed cases here
    if pos is not None:
        fixed_position = True
        pos = np.array(pos, float)
        if pos.shape != (3,):
            raise ValueError(f"pos must be None or a 3-element array-like, got {pos}")
        logger.info(
            "Fixed position    : {:6.1f} {:6.1f} {:6.1f} mm".format(*tuple(1000 * pos))
        )
        if ori is not None:
            ori = np.array(ori, float)
            if ori.shape != (3,):
                raise ValueError(
                    f"oris must be None or a 3-element array-like, got {ori}"
                )
            norm = np.sqrt(np.sum(ori * ori))
            if not np.isclose(norm, 1):
                raise ValueError(f"ori must be a unit vector, got length {norm}")
            logger.info(
                "Fixed orientation  : {:6.4f} {:6.4f} {:6.4f} mm".format(*tuple(ori))
            )
        else:
            logger.info("Free orientation   : <time-varying>")
        fit_n_jobs = 1  # only use 1 job to do the guess fitting
    else:
        fixed_position = False
        # Eventually these could be parameters, but they are just used for
        # the initial grid anyway
        guess_grid = 0.02  # MNE-C uses 0.01, but this is faster w/similar perf
        guess_mindist = max(0.005, min_dist_to_inner_skull)
        guess_exclude = 0.02

        logger.info(f"Guess grid        : {1000 * guess_grid:6.1f} mm")
        if guess_mindist > 0.0:
            logger.info(f"Guess mindist     : {1000 * guess_mindist:6.1f} mm")
        if guess_exclude > 0:
            logger.info(f"Guess exclude     : {1000 * guess_exclude:6.1f} mm")
        logger.info(f"Using {accuracy} MEG coil definitions.")
        fit_n_jobs = n_jobs
    cov = _ensure_cov(cov)
    logger.info("")

    _print_coord_trans(mri_head_t)
    _print_coord_trans(info["dev_head_t"])
    logger.info(f"{len(info['bads'])} bad channels total")

    # Forward model setup (setup_forward_model from setup.c)
    ch_types = evoked.get_channel_types()

    sensors = dict()
    if "grad" in ch_types or "mag" in ch_types:
        sensors["meg"] = _prep_meg_channels(
            info, exclude="bads", accuracy=accuracy, verbose=verbose
        )
    if "eeg" in ch_types:
        sensors["eeg"] = _prep_eeg_channels(info, exclude="bads", verbose=verbose)

    # Ensure that MEG and/or EEG channels are present
    if len(sensors) == 0:
        raise RuntimeError("No MEG or EEG channels found.")

    # Whitener for the data
    logger.info("Decomposing the sensor noise covariance matrix...")
    picks = pick_types(info, meg=True, eeg=True, ref_meg=False)

    # In case we want to more closely match MNE-C for debugging:
    # from ._fiff.pick import pick_info
    # from .cov import prepare_noise_cov
    # info_nb = pick_info(info, picks)
    # cov = prepare_noise_cov(cov, info_nb, info_nb['ch_names'], verbose=False)
    # nzero = (cov['eig'] > 0)
    # n_chan = len(info_nb['ch_names'])
    # whitener = np.zeros((n_chan, n_chan), dtype=np.float64)
    # whitener[nzero, nzero] = 1.0 / np.sqrt(cov['eig'][nzero])
    # whitener = np.dot(whitener, cov['eigvec'])

    whitener, _, rank = compute_whitener(
        cov, info, picks=picks, rank=rank, return_rank=True
    )

    # Proceed to computing the fits (make_guess_data)
    if fixed_position:
        guess_src = dict(nuse=1, rr=pos[np.newaxis], inuse=np.array([True]))
        logger.info("Compute forward for dipole location...")
    else:
        logger.info("\n---- Computing the forward solution for the guesses...")
        guess_src = _make_guesses(
            inner_skull, guess_grid, guess_exclude, guess_mindist, n_jobs=n_jobs
        )[0]
        # grid coordinates go from mri to head frame
        transform_surface_to(guess_src, "head", mri_head_t)
        logger.info("Go through all guess source locations...")

    # inner_skull goes from mri to head frame
    if "rr" in inner_skull:
        transform_surface_to(inner_skull, "head", mri_head_t)
    if fixed_position:
        if "rr" in inner_skull:
            check = _surface_constraint(pos, inner_skull, min_dist_to_inner_skull)
        else:
            check = _sphere_constraint(
                pos,
                inner_skull["r0"],
                R_adj=inner_skull.radius - min_dist_to_inner_skull,
            )
        if check <= 0:
            raise ValueError(
                f"fixed position is {-1000 * check:0.1f}mm outside the inner skull "
                "boundary"
            )

    # C code computes guesses w/sphere model for speed, don't bother here
    fwd_data = _prep_field_computation(
        sensors=sensors, bem=bem, n_jobs=n_jobs, verbose=safe_false
    )
    fwd_data["inner_skull"] = inner_skull
    guess_fwd, guess_fwd_orig, guess_fwd_scales = _dipole_forwards(
        sensors=sensors,
        fwd_data=fwd_data,
        whitener=whitener,
        rr=guess_src["rr"],
        n_jobs=fit_n_jobs,
    )
    # decompose ahead of time
    guess_fwd_svd = [
        _safe_svd(fwd, full_matrices=False)
        for fwd in np.array_split(guess_fwd, len(guess_src["rr"]))
    ]
    guess_data = dict(
        fwd=guess_fwd,
        fwd_svd=guess_fwd_svd,
        fwd_orig=guess_fwd_orig,
        scales=guess_fwd_scales,
    )
    del guess_fwd, guess_fwd_svd, guess_fwd_orig, guess_fwd_scales  # destroyed
    logger.info("[done %d source%s]", guess_src["nuse"], _pl(guess_src["nuse"]))

    # Do actual fits
    data = data[picks]
    ch_names = [info["ch_names"][p] for p in picks]
    proj_op = make_projector(info["projs"], ch_names, info["bads"])[0]
    fun = _fit_dipole_fixed if fixed_position else _fit_dipole
    out = _fit_dipoles(
        fun,
        min_dist_to_inner_skull,
        data,
        times,
        guess_src["rr"],
        guess_data,
        sensors=sensors,
        fwd_data=fwd_data,
        whitener=whitener,
        ori=ori,
        n_jobs=n_jobs,
        rank=rank,
        rhoend=tol,
    )
    assert len(out) == 8
    if fixed_position and ori is not None:
        # DipoleFixed
        data = np.array([out[1], out[3]])
        out_info = deepcopy(info)
        loc = np.concatenate([pos, ori, np.zeros(6)])
        out_info._unlocked = True
        out_info["chs"] = [
            dict(
                ch_name="dip 01",
                loc=loc,
                kind=FIFF.FIFFV_DIPOLE_WAVE,
                coord_frame=FIFF.FIFFV_COORD_UNKNOWN,
                unit=FIFF.FIFF_UNIT_AM,
                coil_type=FIFF.FIFFV_COIL_DIPOLE,
                unit_mul=0,
                range=1,
                cal=1.0,
                scanno=1,
                logno=1,
            ),
            dict(
                ch_name="goodness",
                loc=np.full(12, np.nan),
                kind=FIFF.FIFFV_GOODNESS_FIT,
                unit=FIFF.FIFF_UNIT_AM,
                coord_frame=FIFF.FIFFV_COORD_UNKNOWN,
                coil_type=FIFF.FIFFV_COIL_NONE,
                unit_mul=0,
                range=1.0,
                cal=1.0,
                scanno=2,
                logno=100,
            ),
        ]
        for key in ["hpi_meas", "hpi_results", "projs"]:
            out_info[key] = list()
        for key in [
            "acq_pars",
            "acq_stim",
            "description",
            "dig",
            "experimenter",
            "hpi_subsystem",
            "proj_id",
            "proj_name",
            "subject_info",
        ]:
            out_info[key] = None
        out_info._unlocked = False
        out_info["bads"] = []
        out_info._update_redundant()
        out_info._check_consistency()
        dipoles = DipoleFixed(
            out_info, data, times, evoked.nave, evoked._aspect_kind, comment=comment
        )
    else:
        dipoles = Dipole(
            times, out[0], out[1], out[2], out[3], comment, out[4], out[5], out[6]
        )
    residual = evoked.copy().apply_proj()  # set the projs active
    residual.data[picks] = np.dot(proj_op, out[-1])
    logger.info("%d time points fitted", len(dipoles.times))
    return dipoles, residual


# Every other row of Table 3 from OyamaEtAl2015
_OYAMA = """
0.00 56.29 -27.50
32.50 56.29 5.00
0.00 65.00 5.00
-32.50 56.29 5.00
0.00 56.29 37.50
0.00 32.50 61.29
-56.29 0.00 -27.50
-56.29 32.50 5.00
-65.00 0.00 5.00
-56.29 -32.50 5.00
-56.29 0.00 37.50
-32.50 0.00 61.29
0.00 -56.29 -27.50
-32.50 -56.29 5.00
0.00 -65.00 5.00
32.50 -56.29 5.00
0.00 -56.29 37.50
0.00 -32.50 61.29
56.29 0.00 -27.50
56.29 -32.50 5.00
65.00 0.00 5.00
56.29 32.50 5.00
56.29 0.00 37.50
32.50 0.00 61.29
0.00 0.00 70.00
"""


def get_phantom_dipoles(kind="vectorview"):
    """Get standard phantom dipole locations and orientations.

    Parameters
    ----------
    kind : str
        Get the information for the given system:

            ``vectorview`` (default)
              The Neuromag VectorView phantom.
            ``otaniemi``
              The older Neuromag phantom used at Otaniemi.
            ``oyama``
              The phantom from :footcite:`OyamaEtAl2015`.

        .. versionchanged:: 1.6
           Support added for ``'oyama'``.

    Returns
    -------
    pos : ndarray, shape (n_dipoles, 3)
        The dipole positions.
    ori : ndarray, shape (n_dipoles, 3)
        The dipole orientations.

    See Also
    --------
    mne.datasets.fetch_phantom

    Notes
    -----
    The Elekta phantoms have a radius of 79.5mm, and HPI coil locations
    in the XY-plane at the axis extrema (e.g., (79.5, 0), (0, -79.5), ...).

    References
    ----------
    .. footbibliography::
    """
    _validate_type(kind, str, "kind")
    _check_option("kind", kind, ["vectorview", "otaniemi", "oyama"])
    if kind == "vectorview":
        # these values were pulled from a scanned image provided by
        # Elekta folks
        a = np.array([59.7, 48.6, 35.8, 24.8, 37.2, 27.5, 15.8, 7.9])
        b = np.array([46.1, 41.9, 38.3, 31.5, 13.9, 16.2, 20.0, 19.3])
        x = np.concatenate((a, [0] * 8, -b, [0] * 8))
        y = np.concatenate(([0] * 8, -a, [0] * 8, b))
        c = [22.9, 23.5, 25.5, 23.1, 52.0, 46.4, 41.0, 33.0]
        d = [44.4, 34.0, 21.6, 12.7, 62.4, 51.5, 39.1, 27.9]
        z = np.concatenate((c, c, d, d))
        signs = ([1, -1] * 4 + [-1, 1] * 4) * 2
    elif kind == "otaniemi":
        # these values were pulled from an Neuromag manual
        # (NM20456A, 13.7.1999, p.65)
        a = np.array([56.3, 47.6, 39.0, 30.3])
        b = np.array([32.5, 27.5, 22.5, 17.5])
        c = np.zeros(4)
        x = np.concatenate((a, b, c, c, -a, -b, c, c))
        y = np.concatenate((c, c, -a, -b, c, c, b, a))
        z = np.concatenate((b, a, b, a, b, a, a, b))
        signs = [-1] * 8 + [1] * 16 + [-1] * 8
    else:
        assert kind == "oyama"
        xyz = np.fromstring(_OYAMA.strip().replace("\n", " "), sep=" ").reshape(25, 3)
        xyz = np.repeat(xyz, 2, axis=0)
        x, y, z = xyz.T
        signs = [1] * 50
    pos = np.vstack((x, y, z)).T / 1000.0
    # For Neuromag-style phantoms,
    # Locs are always in XZ or YZ, and so are the oris. The oris are
    # also in the same plane and tangential, so it's easy to determine
    # the orientation.
    # For Oyama, vectors are orthogonal to the position vector and oriented with one
    # pointed toward the north pole (except for the topmost points, which are just xy).
    ori = list()
    for pi, this_pos in enumerate(pos):
        this_ori = np.zeros(3)
        idx = np.where(this_pos == 0)[0]
        # assert len(idx) == 1
        if len(idx) == 0:  # oyama
            idx = [np.argmin(this_pos)]
        idx = np.setdiff1d(np.arange(3), idx[0])
        this_ori[idx] = (this_pos[idx][::-1] / np.linalg.norm(this_pos[idx])) * [1, -1]
        if kind == "oyama":
            # Ensure it's orthogonal to the position vector
            pos_unit = this_pos / np.linalg.norm(this_pos)
            this_ori -= pos_unit * np.dot(this_ori, pos_unit)
            this_ori /= np.linalg.norm(this_ori)
            # This was empirically determined by looking at the dipole fits
            if np.abs(this_ori[2]) >= 1e-6:  # if it's not in the XY plane
                this_ori *= -1 * np.sign(this_ori[2])  # point downward
            elif np.abs(this_ori[0]) < 1e-6:  # in the XY plane (at the north pole)
                this_ori *= -1 * np.sign(this_ori[1])  # point backward
            # Odd ones create a RH coordinate system with their ori
            if pi % 2:
                this_ori = np.cross(pos_unit, this_ori)
        else:
            this_ori *= signs[pi]
        # Now we have this quality, which we could uncomment to
        # double-check:
        # np.testing.assert_allclose(np.dot(this_ori, this_pos) /
        #                            np.linalg.norm(this_pos), 0,
        #                            atol=1e-15)
        ori.append(this_ori)
    ori = np.array(ori)
    return pos, ori


def _concatenate_dipoles(dipoles):
    """Concatenate a list of dipoles."""
    times, pos, amplitude, ori, gof = [], [], [], [], []
    for dipole in dipoles:
        times.append(dipole.times)
        pos.append(dipole.pos)
        amplitude.append(dipole.amplitude)
        ori.append(dipole.ori)
        gof.append(dipole.gof)

    return Dipole(
        np.concatenate(times),
        np.concatenate(pos),
        np.concatenate(amplitude),
        np.concatenate(ori),
        np.concatenate(gof),
        name=None,
    )